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Friday, August 15, 2014

As Math Grows More Complex, Will Computers Reign?

Shalosh B. Ekhad, the co-author of several
papers in respected mathematics journals, has been known to prove with a
single, succinct utterance theorems and identities that previously
required pages of mathematical reasoning. Last year, when asked to
evaluate a formula for the number of integer triangles with a given
perimeter, Ekhad performed 37 calculations in less than a second and
delivered the verdict: “True.”

This simple computation, written with
math software called Maple, verifies a formula for the number of integer
triangles with a given perimeter. (Illustration: Simons Science News)

Shalosh B. Ekhad is a computer. Or, rather, it is any of a rotating
cast of computers used by the mathematician Doron Zeilberger, from the
Dell in his New Jersey office to a supercomputer whose services he
occasionally enlists in Austria. The name — Hebrew for “three B one” —
refers to the AT&T 3B1, Ekhad’s earliest incarnation.

“The soul is the software,” said Zeilberger, who writes his own code using a popular math programming tool called Maple.

Doron Zeilberger, a mathematician at
Rutgers University, believes computers are overtaking humans in their
ability to discover new mathematics. (Photo: Tamar Zeilberger)

A mustachioed, 62-year-old professor at Rutgers University,
Zeilberger anchors one end of a spectrum of opinions about the role of
computers in mathematics. He has been listing Ekhad as a co-author on
papers since the late 1980s “to make a statement that computers should
get credit where credit is due.” For decades, he has railed against
“human-centric bigotry” by mathematicians: a preference for
pencil-and-paper proofs that Zeilberger claims has stymied progress in
the field. “For good reason,” he said. “People feel they will be out of
business.”

Anyone who relies on calculators or
spreadsheets might be surprised to learn that mathematicians have not
universally embraced computers. To many in the field, programming a
machine to prove a triangle identity — or to solve problems that have
yet to be cracked by hand — moves the goalposts of a beloved
3,000-year-old game. Deducing new truths about the mathematical universe
has almost always required intuition, creativity and strokes of genius,
not plugging-and-chugging. In fact, the need to avoid nasty
calculations (for lack of a computer) has often driven discovery,
leading mathematicians to find elegant symbolic techniques like
calculus. To some, the process of unearthing the unexpected, winding
paths of proofs, and discovering new mathematical objects along the way,
is not a means to an end that a computer can replace, but the end
itself.In other words, proofs, where computers are
playing an increasingly prominent role, are not always the end goal of
mathematics. “Many mathematicians think they are building theories with
the ultimate goal of understanding the mathematical universe,” said
Minhyong Kim, a professor of mathematics at Oxford University and Pohang
University of Science and Technology in South Korea. Mathematicians try
to come up with conceptual frameworks that define new objects and state
new conjectures as well as proving old ones. Even when a new theory
yields an important proof, many mathematicians “feel it’s actually the
theory that is more intriguing than the proof itself,” Kim said.Read more... Related linksDoron Zeilberger's homepageDoron Zeilberger(From Wikipedia, the free encyclopedia)Proof confirmed of 400-year-old fruit-stacking problemSource:Quanta Magazine

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Hello, my name is Helge Scherlund and I am the Education Editor and Online Educator of this personal weblog and the founder of eLearning • Computer-Mediated Communication Center.
I have an education in the teaching adults and adult learning from Roskilde University, with Computer-Mediated Communication (CMC) and Human Resource Development (HRD) as specially studied subjects. I am the author of several articles and publications about the use of decision support tools, e-learning and computer-mediated communication. I am a member of The Danish Mathematical Society (DMF), The Danish Society for Theoretical Statistics (DSTS) and an individual member of the European Mathematical Society (EMS). Note: Comments published here are purely my own and do not reflect those of my current or future employers or other organizations.